Question

How many legs are found in one mole of elephants?

Short answer

The total number of legs in one mole of elephants is \( 4 \times 6.022 \times 10^{23} = 2.4088 \times 10^{24} \) legs.

Step-by-step solution

Identify the number of legs on one elephant

Elephants are quadrupeds, which means they have 4 legs each.

Understand the concept of a mole

In the context of this problem, a mole refers to Avogadro's number which is the number 6.022 x 10^23. This is a very large quantity often used in chemistry and physics. In this case, it refers to the number of elephants.

Calculate the total number of legs

Calculate the total number of legs in one mole of elephants by multiplying the number of legs each elephant has (4) by the total number of elephants in a mole (Avogadro's number, 6.022 x 10^23).

Write down the result

Write down the result of the calculation. This is the total number of legs in one mole of elephants.

Key concepts

Understanding Avogadro's Number

At the heart of chemistry lies a fundamental unit known as the mole, similar to how a dozen represents twelve items, a mole represents Avogadro's number of items. Avogadro's number, named after scientist Amedeo Avogadro, is a constant representing the number of atoms or molecules in one mole of a substance, which is precisely \(6.022 \times 10^{23}\).

Why is such a huge number used? At the atomic and molecular level, everything is incredibly tiny, and reactions occur with a vast number of entities. By using Avogadro's number, chemists are able to work with quantities that are meaningful at the human scale. For instance, when we say we have a mole of elephants in the context of the exercise, we imply an enormous quantity equivalent to Avogadro's number of elephants. This whimsical analogy helps students understand the vastness of Avogadro's number in a more concrete manner.

The Basics of Stoichiometry

Stoichiometry is an area of chemistry that involves the quantitative relationships between the reactants and products in a chemical reaction. It allows scientists to predict the amounts of substances consumed and produced in a given reaction.

When it comes to stoichiometry, it's essential to be familiar with the mole concept because reactions happen mole-to-mole, not particle by particle. In other words, stoichiometry uses the balanced chemical equation as a ratio of moles to convert between substances. In our textbook problem, although no chemical reaction is present, the principle of stoichiometry is applied by using the mole concept to relate a known quantity (elephant legs) to a required output (total legs of a mole of elephants). This demonstrates the wide-ranged application of stoichiometric principles beyond typical chemical equations.

Solving Chemical Calculations

Chemical calculations are integral to scientific studies, enabling us to quantify substances and reactions. The calculation process often involves multiple steps, where understanding the relationship between units is crucial.

Referring back to our textbook exercise, we've got a simple mathematical relationship: the number of elephant legs times the number of elephants in one mole. To compute the total legs, we multiply the four legs of one elephant by Avogadro's number. Although this example is simplified and not a chemical reaction, it embodies the fundamental concepts of chemical calculations. Using dimensional analysis, we ensure units cancel out appropriately, leaving us with the desired unit of measurement. In real-world chemistry, the same procedure applies to calculating reactants and products in reactions, where moles, mass, volume, and gas laws come together to solve complex problems.